Since you were in a hole they probably glitched threw a block and either elevated up or just is on the other side of the wall. try digging around the area and if nothing shows try going up from the location.
This morning I killed one at difficulty 1 (I'd been killing them at 10, but people told me difficulty didn't matter) and all I got was regular chicken drops (chicken + feathers) and no message appeared. Is that normal for difficulty 1?
The turkey slicer probably did drop but it just fell into a hole or got stuck in a wall. Was there lava near by? It could have fallen into lava on the other side of a wall.
Like Keliris stated, the Turkey Slicer does not drop every single time a Super Turkey is killed. It drops with the same principle as the Marlix and the Momentus.
It's a 5% base, but looting helps and difficulty might... I'm honestly not sure the impact of difficulty to turkeys but likely applies.
I was on diff 9 (boosting the drop rate) with a voter's sword w/ looting 3 (boosting the drop rate even more). That is probably why I got the slicer.
I believe the turkey slicer automatically goes into your inventory if one is generated, because it is soulbound. Maybe you didn't have enough free inventory slots?